To make a triangle in a circle appoynted whose corners shal
be equall to the corners of any triangle assigned.
When I will draw a triangle in a circle appointed, so that the
corners of that triangle shall be equall to the corners of any
triangle assigned, then must I first draw a tuche lyne vnto that
circle, as the twenty conclusion doth teach, and in the very
poynte of the touche muste I make an angle, equall to one angle
of the triangle, and that inwarde toward the circle: likewise in
the same pricke must I make an other angle w^t the other halfe
of the touche line, equall to an other corner of the triangle
appointed, and then betwen those two corners will there resulte
a third angle, equall to the third corner of that triangle. Nowe
where those two lines that entre into the circle, doo touche the
circumference (beside the touche line) there set I two prickes,
and betwene them I drawe a thyrde line. And so haue I made a
triangle in a circle appointed, whose corners bee equall to the
corners of the triangle assigned.
_Example._
[Illustration]
A.B.C, is the triangle appointed, and F.G.H. is the circle, in
which I muste make an other triangle, with lyke angles to the
angles of A.B.C. the triangle appointed. Therefore fyrst I make
the touch lyne D.F.E. And then make I an angle in F, equall to
A, whiche is one of the angles of the triangle. And the lyne
that maketh that angle with the touche line, is F.H, whiche I
drawe in lengthe vntill it touche the edge of the circle. Then
againe in the same point F, I make an other corner equall to the
angle C. and the line that maketh that corner with the touche
line, is F.G. whiche also I drawe foorthe vntill it touche the
edge of the circle. And then haue I made three angles vpon that
one touch line, and in y^t one point F, and those iij. angles be
equall to the iij. angles of the triangle assigned, whiche
thinge doth plainely appeare, in so muche as they bee equall to
ij. right angles, as you may gesse by the fixt theoreme. And the
thre angles of euerye triangle are equill also to ij. righte
angles, as the two and twenty theoreme dothe show, so that
bicause they be equall to one thirde thinge, they must needes be
equal togither, as the common sentence saith. Then do I draw a
line frome G. to H, and that line maketh a triangle F.G.H, whole
angles be equall to the angles of the triangle appointed. And
this triangle is drawn in a circle, as the conclusion didde
wyll. The proofe of this conclusion doth appeare in the seuenty
and iiij. Theoreme.